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Methods of measuring results in the treatment of cancer
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METHODS
O F M E A S U R I N G R E S U L T S IN T H E TREATMENT OF CANCER BY PERCY STOCKS, C.M.G., M.D., F.R.C.P. CI{IEF MEDICAL STATISTICIAN, GENERAL REGISTER OFFICE
TgE information of greatest interest to the medical statistician in the matter of cancer treatment is the lengthening of life which results from such treatment. This is true also for the physician, surgeon, and radiotherapist, although they must take into account other factors which the statistician cannot measure, such as the patient's prospects of a tolerable life whilst it lasts. T h e chief troubles which arise in statistical studies on this question are of four kinds : (1) T o be sure that when the results of treatments are compared the groups of people treated and compared were initially of the same kind ; (2) T o reduce the number8 of patients lost sight of after treatment to small proportions ; (3) T o differentiate deaths due to cancer from those due to other causes ; and (4) T o apply valid methods of measuring the proportions surviving free of cancer or escaping death from cancer in the various groups. Selection of Patients for T r e a t m e n t . - - T h e first difficulty is to determine what sort and amount of selection was involved in the choosing of patients for a particular kind of treatment. This is expressed very well, as follows, in the fifth Annual Report on the Results of Radiotherapy in Cancer of the Uterine Cervix (i949) , which collates statistics from z4 radiotherapeutic centres in 8 countries. " T h e results presented in this Report will only furnish reliable information as to what can be achieved by radiotherapy if the statements refer to random and unselected samples of patients suffering from cervical cancer ; neither voluntarily nor involuntarily selected material suits the purpose " (p. 237 ). Amongst 2o eentres for which comparison was possible the proportion of patients examined who for one reason or another were not treated ranged from zero to 45 per cent. At ~4 the proportion was 5 per cent or less, at 4 it was between 5 and ~o per cent, and at 2 centres it was greater. It is concluded that " Marked differences in the clinical quality of the material may occur between centres where voluntary selection is practised to a high degree, and centres undertaking treatment of all patients seeking advice for cervical cander within a geographically defined area ". T h e only satisfactory solution of this difficulty about selection will be complete registration and follow-up of e v e r y cancer patient within the geographical area served by the centre, and grouping according to the kind of treatment used. An approach towards this state of affairs has been made by the Liverpool Cancer Control Organization (1948), where in a population of 1"9 millions for the area served in 1947 registrations of new cancer patients in the year were 2.o 4 per moo. Out of the patients referred for treatment of any form of cancer in that area it is concluded that " approximately one-third are beyond effective treatment, one-third are suitable for palliation only, and the remaining one-third comprise the early group in which radical curative treatment is possible " In England and Wales as a whole the total patients being registered under the plan initiated by the National Radium Commission now exceeds 50,000 annually, or about half of the estimated n u m b e r of new cases arising, and these patients are being followed up by the various centres and the records assembled by the General Register Office. Each case is to be followed by calendar years from the time of the first main treatment, each year up to 5, and then at 7, Io, I5 years and after. T h e ultimate aim is to increase the number of centres until virtually all new cases of cancer in the country are being registered. When that position is attained the difficulties about both voluntary and involuntary selection of patients for radiotherapy and surgery will largely disappear, but in the meantime some effort has to be made to extract the m a x i m u m of truth out of records which exist. A valiant attempt to overcome the voluntary selection difficulty has been made in the reports on cancer of the uterine cervix already mentioned. T h e total patients " examined with a view
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to treatment " at each centre for radiotherapy are first recorded, then the numbers not accepteR, and then the numbers accepted but not treated, distinguishing various reasons for this. " Absolute cure " rates are based on the total examined and " relative cure " rates on the total t r e a t e d . The a b s o l u t e rate assumes that none of the patients excluded were alive without evidence of the disease at the end of 5 years ; but since some of them were advised other forms of treatment and some decided to seek treatment elsewhere this rate may be less than the truth and is to be regarded as a m i n i m a l measure of the rate of cure amongst all patients who came for examination in the first instance. T h e r e l a t i v e rate purports to measure the results amongst those actually treated without any assumptions about the others, but a fallacy may arise through the exclusion from it of patients accepted for treatment who did not actually receive it. If this was due to refusal or change of mind by the patient such exclusion is justified; but when it was due to death from cancer occurring before treatment was started or a decision that t h e disease was too far advanced by the time the patient was admitted, such losses may have arisen from defects of organization or from unavoidable delays and should be included as part of the risk of accepting radiological treatment. T h e following examples of statistics from two centres in England taken from the tables of the report on cancer of the uterine cervix illustrate this : - -
X(I933-4I) Y(1932-41) Total patients examined with a view to treatment
762
767
Not accepted
(Operation advised 2371 ~ Unsuitable i
Accepted but not treated
Other reasons ( Patient's decision ~ Prevented by death [ or disease
Alive without evidence of the disease after 5 years
!) 3
56 I4) 22 157
I.I 3 179
At centre X the relative cure rate for the years shown is based upon 7 6 2 - - 5 6 - - 2 2 - - 6 8 4 patients, and at centre Y it would be based on 7 6 7 - - 1 4 - - 3 = 7 5 ° patients. But the fact that 22 failed to start treatment in X compared with only 3 in Y has the effect of improving X ' s relative cure rate in comparison with Y's. T h i s is neither logical n o r desirable, and for the reasons mentioned above patients accepted for treatment b u t prevented by cancer death or advance of the disease from receiving it would be better included amongst the treated total and included in the follow-up tables along with those actually treated. Grouping by S t a g e s . - - T h e definition of stages for cancer of each site is a clinical problem, b u t a few statistical difficulties may be mentioned. T h e report on cancer of the uterine cervix shows that the proportion of cases in Stage-groups I and I I combined ranged from 17 to 85 per cent in the 20 centres, the reasons for this being involuntary selection of and random differences in the patients presenting themselves, and lack of uniformity in the procedure of stage-grouping. The first will depend upon many factors such as the speed with which patients are seen, and sent to the centres ; and provided the stage-grouping is uniform it will not affect statistical comparisons stage b y stage but only the total rates. Lack of uniformity in the stage-grouping is more important since it invalidates the statistics for what are supposed to be comparable groups. I n comparing surgical treatment with radiotherapy it is important that the stage should be fixed before operation and not amended as a result of operative findings. Another difficulty is that where glandular involvement is a criterion for stage-grouping, the finding of such involvement depends a good deal on the amount of care devoted to the examination of glands, and this must be taken into account when framing the definition of stages. T h e constancy of the relative cure rates for Stages I and II
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combined for cancer of the cervix at 7 Scandinavian centres, despite the fact that the proportions of all patients so staged varied from 49 to 65 per cent, suggests that it is possible to achieve reliable statistics of cure of early cases where the definitions of stages are uniformly applied. C o m p l e t e n e s s o f F o l l o w T u p . - - T h e r e is really no satisfactory method of dealing statistically with patients who are lost sight of after being accepted for treatment, and every assumption the statistician makes is open to question. The only way to secure reliable rates of cure or survival is to reduce the numbers lost sight of to small proportions so that the assumption which has to be made has no important effect on the rates. It is worth a great deal of trouble to follow up a few patients and try to ascertain what became of them rather than leave it to the statistician to make corrections of doubtful validity. Nevertheless, there will almost always be a small number of such cases, and it is necessary to decide how to deal with them in the statistics. A common practice is to tabulate the total lost sight of during the whole period of observation for which a rate is to be calculated and leave them in the total forming the denominator of the rate but take no account of them in the survivors forming the numerator. This assumes that none of them were alive (or cancer-free) at the end of the period, which is unnecessarily pessimistic. The more accurate method is to tabulate the numbers falling out of observation in each separate year, allow for their survival during the years preceding and reject t h e m from both the numerator and denominator of the annual survival rate during the year in which they were lost from observation. This can only be done when the ' actuarial ' method to be described below is used. In the report on cancer of the uterine cervix, where the actuarial method has not been used, both the absolute and relative cure rates are prejudiced to some extent by the assumption that none' of the patients lost sight of contributed anything to the numbers surviving. At centre X, for example, as shown above, there were 684 patients treated and I I lost sight of in the first five years. Supposing that 3 fell out in the first year and 2 in each year after, by the actuarial method the numbers at risk to be recorded as dying of cancer during the five successive years would be taken as 68I, 679, 677, 675, 673, instead of assuming that 684 were at risk throughout the period. This matter is referred to again below. D e f i n i t i o n s o f ' C u r e ' a n d ' S u r v i v a l ' . - - T h e r e are several measures of effectiveness of treatment in use and it is necessary to be clear about their definitions. In the records initiated by the Radium Commission from which statistics are being derived at the General Register Office, progress at the end of each year, measuring from the date when the first main treatment began (or from date of registration if no treatment was given), is recorded under the categories : - a. Alive with no evidence of growth. b. Alive with metastases present. c. Alive with growth present at primary site. d. Died during period with growth present at primary site. e. Died during period with metastases present. f. Died during period without evidence of growth. g. Died during period with no information as to persistence of growth. h. Lost sight of during year. A more usual grouping, as used in the report on cancer of the uterine cervix, is into the five categories : - a. Alive without evidence of the disease. b, c. Alive but not cured. D. Died of cancer. E. Died from intercnrrent disease. h. Lost sight of.
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H e r e the information a b o u t cause of death m a y be derived f r o m death certificates, or autopsy records, and the definition of what is m e a n t by dying " f r o m i n t e r c u r r e n t disease " m a y vary. If cancer is m e n t i o n e d on the certificate at all the death often tends to be classified as " died of cancer " ; but a study of death certificates in E n g l a n d and Wales led to an estimate in the Registrar General's Statistical Review for ~938-9 that out of every i o o deaths w i t h m e n t i o n of cancer on the certificate about 15 are said by the certifier to have been due to some o t h e r u n d e r l y i n g cause with cancer as merely a contributory cause. T h i s means that if no account is taken of where cancer is entered on the certificate the " deaths f r o m cancer " will be overstated at the expense of the deaths f r o m i n t e r c u r r e n t disease. E x a m p l e s of this are to be seen in T a b l e X of Dr. Margaret T o d ' s (I949) admirable m o n o g r a p h on the extent to w h i c h cancer patients receive radiotherapy. T h e survival rates there used are derived for the most part f r o m deaths w i t h o u t cancer present, b u t t h e y are t h e n related to the n u m b e r s of deaths in E n g l a n d and Wales certified as " due to " cancer. T h e distinction is particularly i m p o r t a n t for cancer of the skin w h i c h is often present w h e n death was due to another cause.* " D i e d f r o m intercurrent disease " should therefore include all those w h o died of a cause o t h e r than cancer, w h e t h e r or not cancer was present. T h i s m o d e of grouping cannot be deduced f r o m the other one (i.e., f r o m the n u m b e r s in d, e, f, and g) ; it is a different way of looking at the p r o b l e m of survival and can only be p r o p e r l y used if the death certificates are available for examination. W h e n that is the case " died of cancer " should comprise those certificates w h e r e the cancer is entered in Part I of the certificate,'~ and " died of i n t e r c u r r e n t disease " should comprise those w i t h cancer m e n t i o n e d only in Part I I of the certificate and those w i t h no m e n t i o n of cancer. D e a t h s of u n k n o w n cause, for w h i c h certificates are not available and which cannot be classified f r o m other information, should be divided b e t w e e n the two groups in the same p r o p o r t i o n as the k n o w n cases in those groups. I f death should occur f r o m a fresh cancer, of a different site, u n c o n n e c t e d w i t h the one treated, it should be classed as intercurrent disease. T h e r e are two alternative statistical measures of the effectiveness of t r e a t m e n t to be considered, therefore, based u p o n : - I. N u m b e r s who did n o t die of cancer within specified periods from c o m m e n c e m e n t of t r e a t m e n t (i.e., not in category D). 2. N u m b e r s who w e r e a l i v e with no evidence of growth at the end of specified periods from c o m m e n c e m e n t of t r e a t m e n t (i.e., category a). T h e s e are quite different measures, for the first will comprise categories a, b, c, f, and some of d, e, g, whereas the second will comprise only category a. I n addition, w h e n it is n o t possible to ascertain accurately what was the cause of death or w h e t h e r cancer was present, it is possible to fall back u p o n the m e r e fact of being alive, and to use one of the following measures : - 3. N u m b e r of m o n t h s of life experienced after c o m m e n c e m e n t of t r e a t m e n t (or after first recognition of the disease) c o m p a r e d with the n u m b e r of m o n t h s of life expected in the general p o p u l a t i o n of the same sex and age distribution as the groups of cancer patients, according to a s t a n d a r d life stable. * Dr. Tod takes the ratio of cases to deaths for skin cancer as 8, but American statistics for whites make it I7. It follows that Dr. Tod's estimate of 87,ooo new cases of cancer annually in England and Wales is too low. There are other reasons also why this is probable; for example, there is an arithmetical error in the calculations and the survival rates used for some sites (e.g., breast) appear to be unduly conservative. Allowing for these facts the most likely estimate of annual cases seems to be about Ioo,ooo with a possibility of even II0,000. "F"Also, but rarely, where only an ill-defined cause (i.e., included in Sos. 773, 780-795 of the International Statistical Classification of Diseases, x948) appears in Part I, and cancer in Part II.
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4- Total survival rate corrected by allowing for the estimated probability of dying from causes other than cancer in a population having the same age distribution as the group of patients. These methods of arriving at rates will now be considered. Rate o f Escaping Death from C a n c e r . - - T h e term ' s u r v i v a l ' rate cannot properly be applied to the proportion of people who escape dying from one particular cause, since those of them who died of some other cause do not survive. What is to be measured here is the rate of not dying from cancer--that is, of escaping death from cancer--during a period, of time x. A rate which has been widely used under the description " Net Survival Rate " is defined as the ratio : Total alive after x years/Total treated, less sum of those lost sight of and those who died with no evidence of cancer before the end of x years. This is subject to several objections besides the fact that ' survival' here means not having died with cancer present. Those who died cancerfree had been at risk to die of cancer during half the period on the average, but the rate assumes them not to have been at risk at all. Those lost sight of during the x years did not all disappear in the first year, but some were known to have been alive at the end of i, 2, 3, etc., years, and during those years they were at risk to die of cancer, although the rate again ignores this. I f patients were for the most part kept under continuous observation after completion of treatment (an assumption which seems to have been made by Boag (1948) in applying the actuarial method), it would be correct to treat those lost sight of at the end of a year as also being at risk during half that year on the average. Usually, however, inquiries or re-examinations are made only at the end of whole years from the starting date, so it is better to regard those lost sight of during the first year as not at risk during any of that year, those lost sight of during the second year as at risk during the first but not the second year, and so on. T h e allowance to be made is not quite the same as for those who died cancer-free. I t is not possible, therefore, to obtain an accurate rate by jumping straight to x years ; the correct method is to proceed one year at a time, starting each year afresh with the new number at risk, and then multiply together the series of x successive annual rates. This is sometimes described as the " actuarial method ", and it can be equally well applied, and needs to be applied, to the rates of cure dealt with in the next section. There is nothing new in this, for it was pointed out by Greenwood (i926) a long time ago. It became more important, however, when centres began to calculate ten-year survival rates, since the error involved by jumping the x years grows rapidly larger when x exceeds 5. T h e Holt Radium Institute at Manchester began during the second world war, on m y advice, to apply an actuarial method to their calculations of ten-year rates, and explained it in their second Statistical Report issued in 1946 , pp. I 3 I - 5. The method used differed in no essential particular from that used by Greenwood, but differs in one respect from that used by Boag (i948) for comparison with rates of cure obtained by his mathematical method referred to below. It allowed for patients lost sight of during successive years, but on the assumption explained above. An example worked out in the Institute's report related to 62o patients treated in 1932- 3 for cancer of all sites in Stage I of the growth, and that example is repeated below with a somewhat simpler form of presentation, which makes the calculation easier. T h e data between 5 and 7 years, and between 7 and IO years, were not given by separate annual intervals in the report, and in order to illustrate the ideal procedure here the figures at 6, 8, and 9 years have been estimated by assuming there was a uniform distribution of events between the known points (Table [). T h e cumulative rates are then obtained from the last column by successive multiplication (which can be done easily by summing their logarithms) with the following results at 3, 5, 7, and io years (Table H). T h e error involved by the net survival rate method of calculation is seen to become very large. 13
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If data for separate years are not available after 5 years, the follow-up being made only at the end of the seventh and tenth years, the above method can be shortened by treating 5 to 7 and 7 to i o years as single intervals and using the bracketed figures (which are those given in the report). Table
/ . - - C A L C U L A T I O N OF RATES OF ESCAPING D E A T H FROM CANCER IN SUCCESSIVE INTERVALS
YEAR AFTER TREATMENT BEGAN
TREATED PATIENTS _~LIVE AT START OF INTERVAL
NUMBER LOST SIGHT OF DURING INTERVAL
DIED OF INTERCURRENT CAUSE DURING INTERVAL*
POPULATION AT RISK (I,E.~ FOR WHOLE INTERVAL) p=n
ist 2nd 3rd 4th 5th 6th 7th 8th 9th i oth
62o 554 505 464 427 407 368 328 305 282
20
602
8 8
I5 2I 22
--4
i8
546'5 486"5 445 422 385 345 313"5 290-5 z67
22}44 22 II
34
i2]
93
RATE OF ESCAPING DEATH FROM CANCER IN INTERVAL
p-D P
h -E
8 o
II ~2
DIED OF CANCER DURING INTERVAL*
38 34 I2
7 6
3~
"937 "938 "975 "984 "986 -984 "983 "994 "990 "992
* T h e s e descriptions appear in the report but probably the data were in fact " died w ith o u t cancer present ", and " died with cancer".
T h e restllting cumulative rates are then "804 at 7 and "781 at IO, the discrepancy being very slight ; but if the distribution of events over t h e two periods was very irregular the approximation would not be so close. Table //.--CUMULATIVE RATES DERIVEDFROM Table WITH
YEARS AFTER TREATMENT BEGAN
I, COMPARED
CRUDE RATES
I~.ATE OF ESCAPING DEATtI FROM CANCER (CUMULATIVE)
"NET SURVIVAL RATE" FOR COMPARISON
Per u n i t
Pe r cent
3
'857
85"7
5
'83I
83"I
81
7 Io
'804 "785
80"4 78"5
75 69
85
If the data do not differentiate deaths caused by the cancer from those due to some other condition but with cancer present, it is better to use the cancer-free survival rates described in the next section. Rates calculated as in the table above are rates of escaping death from cancer and not rates of escaping death with cancer present. Thug a patient with a skin cancer for whom there is good prospect of many years of life may die of an accident or pneumonia and it is not logical to debit cancer with such a death. FurtKermore the risk of deaths from intercurrent causes increases with advancing age, and if they are included when cancer happens to be present the usual assumption that there is no need to take age into account ceases to be justifiable. This has been pointed out by Boag (i948).
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T o summarize : - i. A rate of escaping death from cancer is suggested. 2. It should be calculated by the actuarial method, multiplying together rates for successive years. 3. After the fifth year, the interval used may be lengthened to 2 and then 3 years without serious error. 4. Deaths from intercurrent disease should include deaths with cancer certified in Part II of the certificate, and deaths from a new independent primary cancer. 5. Deaths whose cause cannot be ascertained should be divided between deaths from cancer and from intercurrent disease in the same proportion as the known cases. 6. The rate for each year (or longer interval after 5 years) is given by
(n--h--D--E)/(n--h -E-)
2 2 where n = n u m b e r alive at beginning of interval, h = n u m b e r lost sight of in interval, D = d i e d from cancer in interval, E = d i e d of intercurrent disease in interval. 7- The number treated should include those accepted for treatment who failed to start treatment through the cancer causing death or being then found too advanced. Cancer-free Survival R a t e s . - - T h e usual method, employed for example in the report on cancer of the uterine cervix, is to express the number alive after 5, 6, 7, etc., years as a percentage of the total who commenced treatment (" relative cure rate ") and as a percentage of the total who applied for treatment (" absolute cure rate "). The difficulties of selection have already been referred to, and the advisability of including in the treated total those accepted for treatment who failed to start because of cancer death or advance of the disease. There are also statistical objections to the usual mode of calculation if the figures purport to measure the rate of keeping alive and free from cancer after treatment. They give an instantaneous cross-section of the position at the end of 5 years, but take no account of the period of time lived during those years by patients who remained free from cancer for i, 2, 3, or 4 years and then died of some intercurrent cause or were lost sight of. The relative cure rate is simply the number of patients in category a at the end of 5, 6, 7, etc., years expressed as a percentage of the original total treated. For example, if out of ioo patients treated 20 die without evidence of growth (category f ) during the first 5 years, they make no contribution to the rate although they were in category a up to death and might all have been there at the end of the 5 years if death from an intercurrent cause had not happened. As a second example, suppose that out of ioo patients treated 50 are alive and cancer-free at the end of 5 years, and that 20 of them die of intercurrent causes between 5 and io years, the rest remaining unchanged ; then the " cure rate " will fall from 5° to 3° per cent although no change in cancer growth has occurred in the interval. Apart from these disadvantages, such " cure rates " depend upon age, since the risk of dying from intercurrent disease increases rapidly with age at the time of life when cancer is frequent, and this may be statistically important when long-period rates are being compared. A treatment centre whose patients have a high average age may be expected to yield rather lower cure rates on that account. To meet these objections a "cancer-free survival rate" is suggested, which would be calculated by the actuarial method in a similar way to the " rate of escaping death from cancer " For this calculation it is unnecessary to tabulate the first 5 years separately, but if the data are available that should be done, though the effect on this rate would usually be slight. After 5 years each year should be set out separately. For purposes of illustration the data from RoswelI Park Memorial Institute, Buffalo, for patients treated for cancer of the uterine cervix in the years I9z9-36 have been taken from pages 68 and 7 ° of the international report already referred to.
(Tables III, IV.)
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The method of calculation is explained by Tables III, IV. Any cases accepted for treatment but prevented from obtaining it by cancer death or advance of the disease are included in N. Those who died during the interval without evidence of cancer are assumed to have been alive without cancer for half the interval on the average. It is assumed, as in the previous calculation, that patients were for the most part not under continuous observation but only seen or reported on at the end of each year, and the correction applied for those lost sight of is based on that assumption. The Table
I/I.--CALCULATION
DIED DURING INTERVAL "WITHOUT CANCER PRESENT
ALIVE WITHOUT CANCER
NUMBER OF TREATED PATIENTS AT START
YEAR AFTER TREATMENT BEGAN
OF CANCER-FREE SURVIVAL RATES I N SUCCESSIVE INTERVALS
AT E N D
OF INTERVAL
ALIVE "WITHOUT CANCER FOR WHOLE INTERVAL
LOST SIGHT OF DURING INTERVAL
N
a+~
i2527
0- 5
6th 7th 8th 9th i oth
344 319 298 275 258
17 12 I0 12 IO 7
49 II
9 7 6 3
247
ah E * D u r i n g first interval 0 - 5 years, ( a + = ) / ( N - o22--); after that (a + 2 5 preceding.
CANCERFREE SURVIVAL RATE IN INTERVAL
f
368"5 324"5 302"5 278" 5 261"O 248'5
"297
'977 "96o "974 I
I
"985 •99 o
)/(a 1 - h ) , w h e r e a 1 is t h e value o f a at e n d o f interval
t I251 patients treated + I a c c e p t e d for treatment b u t prevented by death or disease. The number examined with a v i e w to treatment was I Z 6 i , so the ' absolute ' rate in t h e first interval w o u l d be ,295 , those o f subsequent intervals being unchanged.
cumulative rate is readily obtained by summing the logarithms of the interval rates and converting back to the product. Relative rates are based on the treated cases, and absolute rates on the number applying for treatment. Table I V . - - C u M U L A T I V E
RATES DERIVED FROM
Table III, COMPARED W I T H
CRUDE RATES CANCER-FREE SURVIVAL RATE (CUMULATIVE) YEARS AFTER TREATMENT BEGAN
RELATIVE RATE BASED ON NUMBER TREATED per u n i t
5 7 io
'297 '279 'z65
per cent
29'7 27"9 26"5
CURE RATES AT PRESENT USED
ABSOLUTE RATE BASED ON NUMBER EXAMINED (per cent)
29"5 27"7 26"3
RELATIVE (per cent)
27"5 23"8 19"7
ABSOLUTE (per cent)
z7"3 23"6 19"6
By the end of 7 and IO years there is a large discrepancy between the cure rates, as published at present throughout the international report (Heyman and others, 1949) , and the cancer-free survival rates. Whilst the cure rates are correct as statements of the actual proportion alive without cancer at given moments out of the original total, they cease to be at all reliable as indices of effectiveness of treatment after 5 years have elapsed, and the usefulness of continuing to publish such long-period rates is doubtful. The cancer-free survival rates suggested could be calculated with little difficulty from the data collected by separate centres, wherever that has been done according to the plan Set
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out for the international study of uterine cancer. T h e y could be substituted in future editions of the international report for the all2stage cure rates, but in order to work them for separate stages it would be necessary to obtain data for past years distributing the deaths without cancer, the cases lost sight of, and cases prevented by death or disease from starting treatment, amongst the separate stage groups in which they occurred. T h a t would be a small task for any centre to do, provided the information has been kept, since the numbers to be so distributed would be small. T o summarize : - x. A cancer-free survival rate is suggested which would be free from several fallacies attaching to the present cure rates. 2. It would be calculated by the actuarial method, multiplying together rates for successive periods of time. 3. T h e method is described in the table and could be immediately applied for all-stages rates in the international data set out in the report o n cancer of the uterine cervix, but for the separate stages of growth some additional data would be needed. 4. T h e number treated should include those accepted for treatment who failed to start treatment through the cancer causing death or being then found too advanced. A g e a s a F a c t o r i n t h e R e s u l t s o f T r e a t m e n t . - - I t is generally assumed that age is not important as a factor influencing the chances of remaining cancer-free provided that treatment starts at the same stage of growth. It is assumed that when division is made into stages there is no need to take account of differences in age between groups in so far as it affects the probability of dying from cancer within a given time. This assumption may be justifiable, but it is not strongly founded, and it would be worth while trying to assemble some statistical evidence. It is hoped to do that in the process of time from the records now being collected at the General Register Office, but there may be data already in existence from which 5- or i o-year cancer-free survival rates could be compared at several age groups. Even though it be established that rates of growth, and tendency to secondary or metastatic growth, are not much affected by age, it might still be that the younger the patient the greater the chance of secondary or recurrent growth being noticed quickly and receiving prompt attention. In the discussion of rates in the preceding sections the importance of allowing for the increasing risk of death from intercurrent causes as age advances has been pointed out, and suggestions have been made for reducing to a minimum the effect of this on the rate of escaping death from cancer. It cannot be entirely eliminated, because it is often not a simple matter to decide the underlying cause of death in an elderly patient with cancer present. T h e death certificate attempts to do this, but the difficulty facing the certifier has to be recognized. No one else is in as good a position to decide this matter in most instances. For cancer-free survival rates the distinction required is between deaths with and without cancer present and is more a matter of pathology. Effects of age on the risk of death without cancer present are eliminated, but some slight effect of age on the chance of death with cancer present remains, even though rate of growth is independent of age. When cause of death or condition at the time of death cannot be ascertained, but only the fact of death having occurred, one method is to calculate the normal life expectancies of the groups compared by means of a life table. This is best done by calculating the numbers of months of life expected in 3, 4, 5, 6, etc., years for people of each sex at different ages according to a standard life table based on mortality of the appropriate period. T h e patients in each treatment group are then tabulated in age groups, the numbers multiplied by the months to be expected at the corresponding age, and the total months actually lived by the group during, say, 5 years expressed as a percentage of the total months of life expected in that period. This method has been used in the records from hospitals in the County of London which have been analysed by Harnett in the Reports of the British Empire Cancer Campaign (i94 ° and following years), and is described there.
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It has to be remembered that a life table is based on what would happen if the death-rates for the country as a whole in a given year continued to operate without change. W i t h falling deathrates the survival actually experienced by a population starting from that year is generally rather better than what was expected according to the life t a b l e ; and furthermore life tables are not constructed for every year and the latest available may be based on death-rates of some years back. Consequently the comparison is with an expectation not quite so good as the real one at the time the patients were living. Another difficulty is that cancer treatment data generally relate to groups of people living in a particular part of the country, where the normal expectation of life may be higher or lower than in the country as a whole. For example a national life table gives a poorer survival than would be expected in London. For these reasons it may happen occasionally that the months lived by a group of treated cancer patients exceed the months expected, which causes incredulity. T h a t does not invalidate the method even though there may be a statistically significant excess of actual over expected months of life, showing that it is not merely due to a sampling error. I t is the comparative figures for different groups which are required, not the absolute figures; and if the standard being used for all groups is rather below what it should be, that has no serious effect on the comparison between groups. This method has the advantage of correcting for age differences and is useful where the information about causes of death is not sufficiently reliable to apply one of the other methods. Another method, described by Berkson (1942), is to calculate, from standard death-rates appropriate to the group, t h e probability P0 of not dying from causes other than cancer in the interval. T h e total survival rate experienced, calculated by the cumulative actuarial method, is then divided by P0 to correct for the deaths due to intercurrent causes. M a t h e m a t i c a l E s t i m a t i o n o f Cure Rates f r o m F o r m o f Survival Curve.--Boag (1948) has devised a method of estimating the proportion of cures after treatment before waiting until one has complete data of all patients in the group followed up over 5 or io years. T h e method depends upon constructing a survival curve on logarithmic paper from the start of treatment, using all the data one has up to date no matter for how long the patients have been followed up. This involves a good many assumptions, but it is a very interesting study, and may be very helpful in the future. Before we can reach a conclusion as to its usefulness, however, it will be necessary to test it on good data for cancer of a n u m b e r of sites, giving the exact date of death and presence or absence of cancer in the survivors after known intervals. T h e data now being collected at the General Register Office from cancer centres may prove useful for that, but not until a few years have elapsed. At present this method must be regarded as in the experimental stage, and not as one which can be immediately applied. A good deal more work needs to be done on it. In presenting data, however, it should be borne in mind that exact intervals before death or re-examination must be available for experimental statistical work on this method. It is necessary to know ( i ) those who have died with cancer present at time t, reckoned from the beginning of treatment ; (2) those who have died of some intercurrent disease by time t ; (3) those who remain alive and symptom-free after time t ; and (4) those who remain alive but with cancer present at time t. Boag has suggested how these can be conveniently recorded, and for this reference can be made to his paper. REFERENCES BERKSON, J. (I942), " The Calculation of Survival Rates ", Carcinoma of the Stomach, by Walters, Gray, and
Priestley, Chap. XXII. W . B . Saunders Co. BOAG, J. W. (1948), " The Presentation and Analysis of the Results of Radiotherapy ", Brit. J. Radiol., 21, Nos. 243, 244. BRITISH EMPIRE CANCER CAMPAIGN. Annual Reports for i94 o, and succeeding years. Clinical Cancer Research Committee.
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GREENWOOD, M. (1926), Tile Natural Duration of Cancer. Reports on Public H e a l t h and Medical Subjects, No. 33. L o n d o n : H.N[.S.O. HEYMAN, J., DONALDSON, M., and SCHEFrEY, L. C., ed. (I949) , " Statements of Results obtained in 1941 and previous years (collated in I948): ', Radiotherapy in Cancer of the Uterine Cervix, 5. Stockholm. HOLT RADIUM INSTITUTE (I946), The Results of Radium and X - r a y Therapy in Malignant Disease. e n d Statistical Report, 1934-38. E d i n b u r g h : E. & S. Livingstone, Ltd. LIVERPOOL CANCER CONTROL ORGANIZATION (I948), A n n u a l Report to the National R a d i u m Commission for the year I947. 'REGISTRAR GENERAL'S STATISTICAL REVIEW OF ENGLAND AND WALES (I938--9), Text, 92. TOD, M. (1949), " A n Inquiry into the extent to which Cancer Patients in Great Britain receive Radiotherapy "'. A l t r i n c h a m : J. Sherratt & Son.
SIXTH
INTERNATIONAL CONGRESS LONDON, 195o
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RADIOLOGY,
A REMINDER A coPY of the Preliminary Programme, together with the necessary forms for completion, has been sent to all members of radiologicai societies throughout the world. All those planning to attend are urged to register as Members of the Congress as soon as possible. There are three classes of members : Full Members (including Junior, for those under 3 o) ; Associates accompanying Full Members; and Scientific Associates. All are reminded that a higher fee will be charged for registrations received after April I. Members wishing to read papers must notify the Secretary-General not later than February 15, and an abstract should reach him by April i. Those who have a scientific exhibit to offer must also send details by February 15 . Applications to join one of the tours of Great Britain and Ireland which are being organized for the week following the Congress must be received by February I5. All communications should be sent to the Secretary-General, 6th International Congress of Radiology, 45, Lincoln's Inn Fields, London, W.C.2. Additional copies of the Preliminary Programme can be obtained from the same address on request, stating the language in which they are desired.
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METHODS
O F M E A S U R I N G R E S U L T S IN T H E TREATMENT OF CANCER BY PERCY STOCKS, C.M.G., M.D., F.R.C.P. CI{IEF MEDICAL STATISTICIAN, GENERAL REGISTER OFFICE
TgE information of greatest interest to the medical statistician in the matter of cancer treatment is the lengthening of life which results from such treatment. This is true also for the physician, surgeon, and radiotherapist, although they must take into account other factors which the statistician cannot measure, such as the patient's prospects of a tolerable life whilst it lasts. T h e chief troubles which arise in statistical studies on this question are of four kinds : (1) T o be sure that when the results of treatments are compared the groups of people treated and compared were initially of the same kind ; (2) T o reduce the number8 of patients lost sight of after treatment to small proportions ; (3) T o differentiate deaths due to cancer from those due to other causes ; and (4) T o apply valid methods of measuring the proportions surviving free of cancer or escaping death from cancer in the various groups. Selection of Patients for T r e a t m e n t . - - T h e first difficulty is to determine what sort and amount of selection was involved in the choosing of patients for a particular kind of treatment. This is expressed very well, as follows, in the fifth Annual Report on the Results of Radiotherapy in Cancer of the Uterine Cervix (i949) , which collates statistics from z4 radiotherapeutic centres in 8 countries. " T h e results presented in this Report will only furnish reliable information as to what can be achieved by radiotherapy if the statements refer to random and unselected samples of patients suffering from cervical cancer ; neither voluntarily nor involuntarily selected material suits the purpose " (p. 237 ). Amongst 2o eentres for which comparison was possible the proportion of patients examined who for one reason or another were not treated ranged from zero to 45 per cent. At ~4 the proportion was 5 per cent or less, at 4 it was between 5 and ~o per cent, and at 2 centres it was greater. It is concluded that " Marked differences in the clinical quality of the material may occur between centres where voluntary selection is practised to a high degree, and centres undertaking treatment of all patients seeking advice for cervical cander within a geographically defined area ". T h e only satisfactory solution of this difficulty about selection will be complete registration and follow-up of e v e r y cancer patient within the geographical area served by the centre, and grouping according to the kind of treatment used. An approach towards this state of affairs has been made by the Liverpool Cancer Control Organization (1948), where in a population of 1"9 millions for the area served in 1947 registrations of new cancer patients in the year were 2.o 4 per moo. Out of the patients referred for treatment of any form of cancer in that area it is concluded that " approximately one-third are beyond effective treatment, one-third are suitable for palliation only, and the remaining one-third comprise the early group in which radical curative treatment is possible " In England and Wales as a whole the total patients being registered under the plan initiated by the National Radium Commission now exceeds 50,000 annually, or about half of the estimated n u m b e r of new cases arising, and these patients are being followed up by the various centres and the records assembled by the General Register Office. Each case is to be followed by calendar years from the time of the first main treatment, each year up to 5, and then at 7, Io, I5 years and after. T h e ultimate aim is to increase the number of centres until virtually all new cases of cancer in the country are being registered. When that position is attained the difficulties about both voluntary and involuntary selection of patients for radiotherapy and surgery will largely disappear, but in the meantime some effort has to be made to extract the m a x i m u m of truth out of records which exist. A valiant attempt to overcome the voluntary selection difficulty has been made in the reports on cancer of the uterine cervix already mentioned. T h e total patients " examined with a view
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to treatment " at each centre for radiotherapy are first recorded, then the numbers not accepteR, and then the numbers accepted but not treated, distinguishing various reasons for this. " Absolute cure " rates are based on the total examined and " relative cure " rates on the total t r e a t e d . The a b s o l u t e rate assumes that none of the patients excluded were alive without evidence of the disease at the end of 5 years ; but since some of them were advised other forms of treatment and some decided to seek treatment elsewhere this rate may be less than the truth and is to be regarded as a m i n i m a l measure of the rate of cure amongst all patients who came for examination in the first instance. T h e r e l a t i v e rate purports to measure the results amongst those actually treated without any assumptions about the others, but a fallacy may arise through the exclusion from it of patients accepted for treatment who did not actually receive it. If this was due to refusal or change of mind by the patient such exclusion is justified; but when it was due to death from cancer occurring before treatment was started or a decision that t h e disease was too far advanced by the time the patient was admitted, such losses may have arisen from defects of organization or from unavoidable delays and should be included as part of the risk of accepting radiological treatment. T h e following examples of statistics from two centres in England taken from the tables of the report on cancer of the uterine cervix illustrate this : - -
X(I933-4I) Y(1932-41) Total patients examined with a view to treatment
762
767
Not accepted
(Operation advised 2371 ~ Unsuitable i
Accepted but not treated
Other reasons ( Patient's decision ~ Prevented by death [ or disease
Alive without evidence of the disease after 5 years
!) 3
56 I4) 22 157
I.I 3 179
At centre X the relative cure rate for the years shown is based upon 7 6 2 - - 5 6 - - 2 2 - - 6 8 4 patients, and at centre Y it would be based on 7 6 7 - - 1 4 - - 3 = 7 5 ° patients. But the fact that 22 failed to start treatment in X compared with only 3 in Y has the effect of improving X ' s relative cure rate in comparison with Y's. T h i s is neither logical n o r desirable, and for the reasons mentioned above patients accepted for treatment b u t prevented by cancer death or advance of the disease from receiving it would be better included amongst the treated total and included in the follow-up tables along with those actually treated. Grouping by S t a g e s . - - T h e definition of stages for cancer of each site is a clinical problem, b u t a few statistical difficulties may be mentioned. T h e report on cancer of the uterine cervix shows that the proportion of cases in Stage-groups I and I I combined ranged from 17 to 85 per cent in the 20 centres, the reasons for this being involuntary selection of and random differences in the patients presenting themselves, and lack of uniformity in the procedure of stage-grouping. The first will depend upon many factors such as the speed with which patients are seen, and sent to the centres ; and provided the stage-grouping is uniform it will not affect statistical comparisons stage b y stage but only the total rates. Lack of uniformity in the stage-grouping is more important since it invalidates the statistics for what are supposed to be comparable groups. I n comparing surgical treatment with radiotherapy it is important that the stage should be fixed before operation and not amended as a result of operative findings. Another difficulty is that where glandular involvement is a criterion for stage-grouping, the finding of such involvement depends a good deal on the amount of care devoted to the examination of glands, and this must be taken into account when framing the definition of stages. T h e constancy of the relative cure rates for Stages I and II
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i8 9
combined for cancer of the cervix at 7 Scandinavian centres, despite the fact that the proportions of all patients so staged varied from 49 to 65 per cent, suggests that it is possible to achieve reliable statistics of cure of early cases where the definitions of stages are uniformly applied. C o m p l e t e n e s s o f F o l l o w T u p . - - T h e r e is really no satisfactory method of dealing statistically with patients who are lost sight of after being accepted for treatment, and every assumption the statistician makes is open to question. The only way to secure reliable rates of cure or survival is to reduce the numbers lost sight of to small proportions so that the assumption which has to be made has no important effect on the rates. It is worth a great deal of trouble to follow up a few patients and try to ascertain what became of them rather than leave it to the statistician to make corrections of doubtful validity. Nevertheless, there will almost always be a small number of such cases, and it is necessary to decide how to deal with them in the statistics. A common practice is to tabulate the total lost sight of during the whole period of observation for which a rate is to be calculated and leave them in the total forming the denominator of the rate but take no account of them in the survivors forming the numerator. This assumes that none of them were alive (or cancer-free) at the end of the period, which is unnecessarily pessimistic. The more accurate method is to tabulate the numbers falling out of observation in each separate year, allow for their survival during the years preceding and reject t h e m from both the numerator and denominator of the annual survival rate during the year in which they were lost from observation. This can only be done when the ' actuarial ' method to be described below is used. In the report on cancer of the uterine cervix, where the actuarial method has not been used, both the absolute and relative cure rates are prejudiced to some extent by the assumption that none' of the patients lost sight of contributed anything to the numbers surviving. At centre X, for example, as shown above, there were 684 patients treated and I I lost sight of in the first five years. Supposing that 3 fell out in the first year and 2 in each year after, by the actuarial method the numbers at risk to be recorded as dying of cancer during the five successive years would be taken as 68I, 679, 677, 675, 673, instead of assuming that 684 were at risk throughout the period. This matter is referred to again below. D e f i n i t i o n s o f ' C u r e ' a n d ' S u r v i v a l ' . - - T h e r e are several measures of effectiveness of treatment in use and it is necessary to be clear about their definitions. In the records initiated by the Radium Commission from which statistics are being derived at the General Register Office, progress at the end of each year, measuring from the date when the first main treatment began (or from date of registration if no treatment was given), is recorded under the categories : - a. Alive with no evidence of growth. b. Alive with metastases present. c. Alive with growth present at primary site. d. Died during period with growth present at primary site. e. Died during period with metastases present. f. Died during period without evidence of growth. g. Died during period with no information as to persistence of growth. h. Lost sight of during year. A more usual grouping, as used in the report on cancer of the uterine cervix, is into the five categories : - a. Alive without evidence of the disease. b, c. Alive but not cured. D. Died of cancer. E. Died from intercnrrent disease. h. Lost sight of.
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H e r e the information a b o u t cause of death m a y be derived f r o m death certificates, or autopsy records, and the definition of what is m e a n t by dying " f r o m i n t e r c u r r e n t disease " m a y vary. If cancer is m e n t i o n e d on the certificate at all the death often tends to be classified as " died of cancer " ; but a study of death certificates in E n g l a n d and Wales led to an estimate in the Registrar General's Statistical Review for ~938-9 that out of every i o o deaths w i t h m e n t i o n of cancer on the certificate about 15 are said by the certifier to have been due to some o t h e r u n d e r l y i n g cause with cancer as merely a contributory cause. T h i s means that if no account is taken of where cancer is entered on the certificate the " deaths f r o m cancer " will be overstated at the expense of the deaths f r o m i n t e r c u r r e n t disease. E x a m p l e s of this are to be seen in T a b l e X of Dr. Margaret T o d ' s (I949) admirable m o n o g r a p h on the extent to w h i c h cancer patients receive radiotherapy. T h e survival rates there used are derived for the most part f r o m deaths w i t h o u t cancer present, b u t t h e y are t h e n related to the n u m b e r s of deaths in E n g l a n d and Wales certified as " due to " cancer. T h e distinction is particularly i m p o r t a n t for cancer of the skin w h i c h is often present w h e n death was due to another cause.* " D i e d f r o m intercurrent disease " should therefore include all those w h o died of a cause o t h e r than cancer, w h e t h e r or not cancer was present. T h i s m o d e of grouping cannot be deduced f r o m the other one (i.e., f r o m the n u m b e r s in d, e, f, and g) ; it is a different way of looking at the p r o b l e m of survival and can only be p r o p e r l y used if the death certificates are available for examination. W h e n that is the case " died of cancer " should comprise those certificates w h e r e the cancer is entered in Part I of the certificate,'~ and " died of i n t e r c u r r e n t disease " should comprise those w i t h cancer m e n t i o n e d only in Part I I of the certificate and those w i t h no m e n t i o n of cancer. D e a t h s of u n k n o w n cause, for w h i c h certificates are not available and which cannot be classified f r o m other information, should be divided b e t w e e n the two groups in the same p r o p o r t i o n as the k n o w n cases in those groups. I f death should occur f r o m a fresh cancer, of a different site, u n c o n n e c t e d w i t h the one treated, it should be classed as intercurrent disease. T h e r e are two alternative statistical measures of the effectiveness of t r e a t m e n t to be considered, therefore, based u p o n : - I. N u m b e r s who did n o t die of cancer within specified periods from c o m m e n c e m e n t of t r e a t m e n t (i.e., not in category D). 2. N u m b e r s who w e r e a l i v e with no evidence of growth at the end of specified periods from c o m m e n c e m e n t of t r e a t m e n t (i.e., category a). T h e s e are quite different measures, for the first will comprise categories a, b, c, f, and some of d, e, g, whereas the second will comprise only category a. I n addition, w h e n it is n o t possible to ascertain accurately what was the cause of death or w h e t h e r cancer was present, it is possible to fall back u p o n the m e r e fact of being alive, and to use one of the following measures : - 3. N u m b e r of m o n t h s of life experienced after c o m m e n c e m e n t of t r e a t m e n t (or after first recognition of the disease) c o m p a r e d with the n u m b e r of m o n t h s of life expected in the general p o p u l a t i o n of the same sex and age distribution as the groups of cancer patients, according to a s t a n d a r d life stable. * Dr. Tod takes the ratio of cases to deaths for skin cancer as 8, but American statistics for whites make it I7. It follows that Dr. Tod's estimate of 87,ooo new cases of cancer annually in England and Wales is too low. There are other reasons also why this is probable; for example, there is an arithmetical error in the calculations and the survival rates used for some sites (e.g., breast) appear to be unduly conservative. Allowing for these facts the most likely estimate of annual cases seems to be about Ioo,ooo with a possibility of even II0,000. "F"Also, but rarely, where only an ill-defined cause (i.e., included in Sos. 773, 780-795 of the International Statistical Classification of Diseases, x948) appears in Part I, and cancer in Part II.
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191
4- Total survival rate corrected by allowing for the estimated probability of dying from causes other than cancer in a population having the same age distribution as the group of patients. These methods of arriving at rates will now be considered. Rate o f Escaping Death from C a n c e r . - - T h e term ' s u r v i v a l ' rate cannot properly be applied to the proportion of people who escape dying from one particular cause, since those of them who died of some other cause do not survive. What is to be measured here is the rate of not dying from cancer--that is, of escaping death from cancer--during a period, of time x. A rate which has been widely used under the description " Net Survival Rate " is defined as the ratio : Total alive after x years/Total treated, less sum of those lost sight of and those who died with no evidence of cancer before the end of x years. This is subject to several objections besides the fact that ' survival' here means not having died with cancer present. Those who died cancerfree had been at risk to die of cancer during half the period on the average, but the rate assumes them not to have been at risk at all. Those lost sight of during the x years did not all disappear in the first year, but some were known to have been alive at the end of i, 2, 3, etc., years, and during those years they were at risk to die of cancer, although the rate again ignores this. I f patients were for the most part kept under continuous observation after completion of treatment (an assumption which seems to have been made by Boag (1948) in applying the actuarial method), it would be correct to treat those lost sight of at the end of a year as also being at risk during half that year on the average. Usually, however, inquiries or re-examinations are made only at the end of whole years from the starting date, so it is better to regard those lost sight of during the first year as not at risk during any of that year, those lost sight of during the second year as at risk during the first but not the second year, and so on. T h e allowance to be made is not quite the same as for those who died cancer-free. I t is not possible, therefore, to obtain an accurate rate by jumping straight to x years ; the correct method is to proceed one year at a time, starting each year afresh with the new number at risk, and then multiply together the series of x successive annual rates. This is sometimes described as the " actuarial method ", and it can be equally well applied, and needs to be applied, to the rates of cure dealt with in the next section. There is nothing new in this, for it was pointed out by Greenwood (i926) a long time ago. It became more important, however, when centres began to calculate ten-year survival rates, since the error involved by jumping the x years grows rapidly larger when x exceeds 5. T h e Holt Radium Institute at Manchester began during the second world war, on m y advice, to apply an actuarial method to their calculations of ten-year rates, and explained it in their second Statistical Report issued in 1946 , pp. I 3 I - 5. The method used differed in no essential particular from that used by Greenwood, but differs in one respect from that used by Boag (i948) for comparison with rates of cure obtained by his mathematical method referred to below. It allowed for patients lost sight of during successive years, but on the assumption explained above. An example worked out in the Institute's report related to 62o patients treated in 1932- 3 for cancer of all sites in Stage I of the growth, and that example is repeated below with a somewhat simpler form of presentation, which makes the calculation easier. T h e data between 5 and 7 years, and between 7 and IO years, were not given by separate annual intervals in the report, and in order to illustrate the ideal procedure here the figures at 6, 8, and 9 years have been estimated by assuming there was a uniform distribution of events between the known points (Table [). T h e cumulative rates are then obtained from the last column by successive multiplication (which can be done easily by summing their logarithms) with the following results at 3, 5, 7, and io years (Table H). T h e error involved by the net survival rate method of calculation is seen to become very large. 13
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If data for separate years are not available after 5 years, the follow-up being made only at the end of the seventh and tenth years, the above method can be shortened by treating 5 to 7 and 7 to i o years as single intervals and using the bracketed figures (which are those given in the report). Table
/ . - - C A L C U L A T I O N OF RATES OF ESCAPING D E A T H FROM CANCER IN SUCCESSIVE INTERVALS
YEAR AFTER TREATMENT BEGAN
TREATED PATIENTS _~LIVE AT START OF INTERVAL
NUMBER LOST SIGHT OF DURING INTERVAL
DIED OF INTERCURRENT CAUSE DURING INTERVAL*
POPULATION AT RISK (I,E.~ FOR WHOLE INTERVAL) p=n
ist 2nd 3rd 4th 5th 6th 7th 8th 9th i oth
62o 554 505 464 427 407 368 328 305 282
20
602
8 8
I5 2I 22
--4
i8
546'5 486"5 445 422 385 345 313"5 290-5 z67
22}44 22 II
34
i2]
93
RATE OF ESCAPING DEATH FROM CANCER IN INTERVAL
p-D P
h -E
8 o
II ~2
DIED OF CANCER DURING INTERVAL*
38 34 I2
7 6
3~
"937 "938 "975 "984 "986 -984 "983 "994 "990 "992
* T h e s e descriptions appear in the report but probably the data were in fact " died w ith o u t cancer present ", and " died with cancer".
T h e restllting cumulative rates are then "804 at 7 and "781 at IO, the discrepancy being very slight ; but if the distribution of events over t h e two periods was very irregular the approximation would not be so close. Table //.--CUMULATIVE RATES DERIVEDFROM Table WITH
YEARS AFTER TREATMENT BEGAN
I, COMPARED
CRUDE RATES
I~.ATE OF ESCAPING DEATtI FROM CANCER (CUMULATIVE)
"NET SURVIVAL RATE" FOR COMPARISON
Per u n i t
Pe r cent
3
'857
85"7
5
'83I
83"I
81
7 Io
'804 "785
80"4 78"5
75 69
85
If the data do not differentiate deaths caused by the cancer from those due to some other condition but with cancer present, it is better to use the cancer-free survival rates described in the next section. Rates calculated as in the table above are rates of escaping death from cancer and not rates of escaping death with cancer present. Thug a patient with a skin cancer for whom there is good prospect of many years of life may die of an accident or pneumonia and it is not logical to debit cancer with such a death. FurtKermore the risk of deaths from intercurrent causes increases with advancing age, and if they are included when cancer happens to be present the usual assumption that there is no need to take age into account ceases to be justifiable. This has been pointed out by Boag (i948).
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T o summarize : - i. A rate of escaping death from cancer is suggested. 2. It should be calculated by the actuarial method, multiplying together rates for successive years. 3. After the fifth year, the interval used may be lengthened to 2 and then 3 years without serious error. 4. Deaths from intercurrent disease should include deaths with cancer certified in Part II of the certificate, and deaths from a new independent primary cancer. 5. Deaths whose cause cannot be ascertained should be divided between deaths from cancer and from intercurrent disease in the same proportion as the known cases. 6. The rate for each year (or longer interval after 5 years) is given by
(n--h--D--E)/(n--h -E-)
2 2 where n = n u m b e r alive at beginning of interval, h = n u m b e r lost sight of in interval, D = d i e d from cancer in interval, E = d i e d of intercurrent disease in interval. 7- The number treated should include those accepted for treatment who failed to start treatment through the cancer causing death or being then found too advanced. Cancer-free Survival R a t e s . - - T h e usual method, employed for example in the report on cancer of the uterine cervix, is to express the number alive after 5, 6, 7, etc., years as a percentage of the total who commenced treatment (" relative cure rate ") and as a percentage of the total who applied for treatment (" absolute cure rate "). The difficulties of selection have already been referred to, and the advisability of including in the treated total those accepted for treatment who failed to start because of cancer death or advance of the disease. There are also statistical objections to the usual mode of calculation if the figures purport to measure the rate of keeping alive and free from cancer after treatment. They give an instantaneous cross-section of the position at the end of 5 years, but take no account of the period of time lived during those years by patients who remained free from cancer for i, 2, 3, or 4 years and then died of some intercurrent cause or were lost sight of. The relative cure rate is simply the number of patients in category a at the end of 5, 6, 7, etc., years expressed as a percentage of the original total treated. For example, if out of ioo patients treated 20 die without evidence of growth (category f ) during the first 5 years, they make no contribution to the rate although they were in category a up to death and might all have been there at the end of the 5 years if death from an intercurrent cause had not happened. As a second example, suppose that out of ioo patients treated 50 are alive and cancer-free at the end of 5 years, and that 20 of them die of intercurrent causes between 5 and io years, the rest remaining unchanged ; then the " cure rate " will fall from 5° to 3° per cent although no change in cancer growth has occurred in the interval. Apart from these disadvantages, such " cure rates " depend upon age, since the risk of dying from intercurrent disease increases rapidly with age at the time of life when cancer is frequent, and this may be statistically important when long-period rates are being compared. A treatment centre whose patients have a high average age may be expected to yield rather lower cure rates on that account. To meet these objections a "cancer-free survival rate" is suggested, which would be calculated by the actuarial method in a similar way to the " rate of escaping death from cancer " For this calculation it is unnecessary to tabulate the first 5 years separately, but if the data are available that should be done, though the effect on this rate would usually be slight. After 5 years each year should be set out separately. For purposes of illustration the data from RoswelI Park Memorial Institute, Buffalo, for patients treated for cancer of the uterine cervix in the years I9z9-36 have been taken from pages 68 and 7 ° of the international report already referred to.
(Tables III, IV.)
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The method of calculation is explained by Tables III, IV. Any cases accepted for treatment but prevented from obtaining it by cancer death or advance of the disease are included in N. Those who died during the interval without evidence of cancer are assumed to have been alive without cancer for half the interval on the average. It is assumed, as in the previous calculation, that patients were for the most part not under continuous observation but only seen or reported on at the end of each year, and the correction applied for those lost sight of is based on that assumption. The Table
I/I.--CALCULATION
DIED DURING INTERVAL "WITHOUT CANCER PRESENT
ALIVE WITHOUT CANCER
NUMBER OF TREATED PATIENTS AT START
YEAR AFTER TREATMENT BEGAN
OF CANCER-FREE SURVIVAL RATES I N SUCCESSIVE INTERVALS
AT E N D
OF INTERVAL
ALIVE "WITHOUT CANCER FOR WHOLE INTERVAL
LOST SIGHT OF DURING INTERVAL
N
a+~
i2527
0- 5
6th 7th 8th 9th i oth
344 319 298 275 258
17 12 I0 12 IO 7
49 II
9 7 6 3
247
ah E * D u r i n g first interval 0 - 5 years, ( a + = ) / ( N - o22--); after that (a + 2 5 preceding.
CANCERFREE SURVIVAL RATE IN INTERVAL
f
368"5 324"5 302"5 278" 5 261"O 248'5
"297
'977 "96o "974 I
I
"985 •99 o
)/(a 1 - h ) , w h e r e a 1 is t h e value o f a at e n d o f interval
t I251 patients treated + I a c c e p t e d for treatment b u t prevented by death or disease. The number examined with a v i e w to treatment was I Z 6 i , so the ' absolute ' rate in t h e first interval w o u l d be ,295 , those o f subsequent intervals being unchanged.
cumulative rate is readily obtained by summing the logarithms of the interval rates and converting back to the product. Relative rates are based on the treated cases, and absolute rates on the number applying for treatment. Table I V . - - C u M U L A T I V E
RATES DERIVED FROM
Table III, COMPARED W I T H
CRUDE RATES CANCER-FREE SURVIVAL RATE (CUMULATIVE) YEARS AFTER TREATMENT BEGAN
RELATIVE RATE BASED ON NUMBER TREATED per u n i t
5 7 io
'297 '279 'z65
per cent
29'7 27"9 26"5
CURE RATES AT PRESENT USED
ABSOLUTE RATE BASED ON NUMBER EXAMINED (per cent)
29"5 27"7 26"3
RELATIVE (per cent)
27"5 23"8 19"7
ABSOLUTE (per cent)
z7"3 23"6 19"6
By the end of 7 and IO years there is a large discrepancy between the cure rates, as published at present throughout the international report (Heyman and others, 1949) , and the cancer-free survival rates. Whilst the cure rates are correct as statements of the actual proportion alive without cancer at given moments out of the original total, they cease to be at all reliable as indices of effectiveness of treatment after 5 years have elapsed, and the usefulness of continuing to publish such long-period rates is doubtful. The cancer-free survival rates suggested could be calculated with little difficulty from the data collected by separate centres, wherever that has been done according to the plan Set
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out for the international study of uterine cancer. T h e y could be substituted in future editions of the international report for the all2stage cure rates, but in order to work them for separate stages it would be necessary to obtain data for past years distributing the deaths without cancer, the cases lost sight of, and cases prevented by death or disease from starting treatment, amongst the separate stage groups in which they occurred. T h a t would be a small task for any centre to do, provided the information has been kept, since the numbers to be so distributed would be small. T o summarize : - x. A cancer-free survival rate is suggested which would be free from several fallacies attaching to the present cure rates. 2. It would be calculated by the actuarial method, multiplying together rates for successive periods of time. 3. T h e method is described in the table and could be immediately applied for all-stages rates in the international data set out in the report o n cancer of the uterine cervix, but for the separate stages of growth some additional data would be needed. 4. T h e number treated should include those accepted for treatment who failed to start treatment through the cancer causing death or being then found too advanced. A g e a s a F a c t o r i n t h e R e s u l t s o f T r e a t m e n t . - - I t is generally assumed that age is not important as a factor influencing the chances of remaining cancer-free provided that treatment starts at the same stage of growth. It is assumed that when division is made into stages there is no need to take account of differences in age between groups in so far as it affects the probability of dying from cancer within a given time. This assumption may be justifiable, but it is not strongly founded, and it would be worth while trying to assemble some statistical evidence. It is hoped to do that in the process of time from the records now being collected at the General Register Office, but there may be data already in existence from which 5- or i o-year cancer-free survival rates could be compared at several age groups. Even though it be established that rates of growth, and tendency to secondary or metastatic growth, are not much affected by age, it might still be that the younger the patient the greater the chance of secondary or recurrent growth being noticed quickly and receiving prompt attention. In the discussion of rates in the preceding sections the importance of allowing for the increasing risk of death from intercurrent causes as age advances has been pointed out, and suggestions have been made for reducing to a minimum the effect of this on the rate of escaping death from cancer. It cannot be entirely eliminated, because it is often not a simple matter to decide the underlying cause of death in an elderly patient with cancer present. T h e death certificate attempts to do this, but the difficulty facing the certifier has to be recognized. No one else is in as good a position to decide this matter in most instances. For cancer-free survival rates the distinction required is between deaths with and without cancer present and is more a matter of pathology. Effects of age on the risk of death without cancer present are eliminated, but some slight effect of age on the chance of death with cancer present remains, even though rate of growth is independent of age. When cause of death or condition at the time of death cannot be ascertained, but only the fact of death having occurred, one method is to calculate the normal life expectancies of the groups compared by means of a life table. This is best done by calculating the numbers of months of life expected in 3, 4, 5, 6, etc., years for people of each sex at different ages according to a standard life table based on mortality of the appropriate period. T h e patients in each treatment group are then tabulated in age groups, the numbers multiplied by the months to be expected at the corresponding age, and the total months actually lived by the group during, say, 5 years expressed as a percentage of the total months of life expected in that period. This method has been used in the records from hospitals in the County of London which have been analysed by Harnett in the Reports of the British Empire Cancer Campaign (i94 ° and following years), and is described there.
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It has to be remembered that a life table is based on what would happen if the death-rates for the country as a whole in a given year continued to operate without change. W i t h falling deathrates the survival actually experienced by a population starting from that year is generally rather better than what was expected according to the life t a b l e ; and furthermore life tables are not constructed for every year and the latest available may be based on death-rates of some years back. Consequently the comparison is with an expectation not quite so good as the real one at the time the patients were living. Another difficulty is that cancer treatment data generally relate to groups of people living in a particular part of the country, where the normal expectation of life may be higher or lower than in the country as a whole. For example a national life table gives a poorer survival than would be expected in London. For these reasons it may happen occasionally that the months lived by a group of treated cancer patients exceed the months expected, which causes incredulity. T h a t does not invalidate the method even though there may be a statistically significant excess of actual over expected months of life, showing that it is not merely due to a sampling error. I t is the comparative figures for different groups which are required, not the absolute figures; and if the standard being used for all groups is rather below what it should be, that has no serious effect on the comparison between groups. This method has the advantage of correcting for age differences and is useful where the information about causes of death is not sufficiently reliable to apply one of the other methods. Another method, described by Berkson (1942), is to calculate, from standard death-rates appropriate to the group, t h e probability P0 of not dying from causes other than cancer in the interval. T h e total survival rate experienced, calculated by the cumulative actuarial method, is then divided by P0 to correct for the deaths due to intercurrent causes. M a t h e m a t i c a l E s t i m a t i o n o f Cure Rates f r o m F o r m o f Survival Curve.--Boag (1948) has devised a method of estimating the proportion of cures after treatment before waiting until one has complete data of all patients in the group followed up over 5 or io years. T h e method depends upon constructing a survival curve on logarithmic paper from the start of treatment, using all the data one has up to date no matter for how long the patients have been followed up. This involves a good many assumptions, but it is a very interesting study, and may be very helpful in the future. Before we can reach a conclusion as to its usefulness, however, it will be necessary to test it on good data for cancer of a n u m b e r of sites, giving the exact date of death and presence or absence of cancer in the survivors after known intervals. T h e data now being collected at the General Register Office from cancer centres may prove useful for that, but not until a few years have elapsed. At present this method must be regarded as in the experimental stage, and not as one which can be immediately applied. A good deal more work needs to be done on it. In presenting data, however, it should be borne in mind that exact intervals before death or re-examination must be available for experimental statistical work on this method. It is necessary to know ( i ) those who have died with cancer present at time t, reckoned from the beginning of treatment ; (2) those who have died of some intercurrent disease by time t ; (3) those who remain alive and symptom-free after time t ; and (4) those who remain alive but with cancer present at time t. Boag has suggested how these can be conveniently recorded, and for this reference can be made to his paper. REFERENCES BERKSON, J. (I942), " The Calculation of Survival Rates ", Carcinoma of the Stomach, by Walters, Gray, and
Priestley, Chap. XXII. W . B . Saunders Co. BOAG, J. W. (1948), " The Presentation and Analysis of the Results of Radiotherapy ", Brit. J. Radiol., 21, Nos. 243, 244. BRITISH EMPIRE CANCER CAMPAIGN. Annual Reports for i94 o, and succeeding years. Clinical Cancer Research Committee.
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GREENWOOD, M. (1926), Tile Natural Duration of Cancer. Reports on Public H e a l t h and Medical Subjects, No. 33. L o n d o n : H.N[.S.O. HEYMAN, J., DONALDSON, M., and SCHEFrEY, L. C., ed. (I949) , " Statements of Results obtained in 1941 and previous years (collated in I948): ', Radiotherapy in Cancer of the Uterine Cervix, 5. Stockholm. HOLT RADIUM INSTITUTE (I946), The Results of Radium and X - r a y Therapy in Malignant Disease. e n d Statistical Report, 1934-38. E d i n b u r g h : E. & S. Livingstone, Ltd. LIVERPOOL CANCER CONTROL ORGANIZATION (I948), A n n u a l Report to the National R a d i u m Commission for the year I947. 'REGISTRAR GENERAL'S STATISTICAL REVIEW OF ENGLAND AND WALES (I938--9), Text, 92. TOD, M. (1949), " A n Inquiry into the extent to which Cancer Patients in Great Britain receive Radiotherapy "'. A l t r i n c h a m : J. Sherratt & Son.
SIXTH
INTERNATIONAL CONGRESS LONDON, 195o
OF
RADIOLOGY,
A REMINDER A coPY of the Preliminary Programme, together with the necessary forms for completion, has been sent to all members of radiologicai societies throughout the world. All those planning to attend are urged to register as Members of the Congress as soon as possible. There are three classes of members : Full Members (including Junior, for those under 3 o) ; Associates accompanying Full Members; and Scientific Associates. All are reminded that a higher fee will be charged for registrations received after April I. Members wishing to read papers must notify the Secretary-General not later than February 15, and an abstract should reach him by April i. Those who have a scientific exhibit to offer must also send details by February 15 . Applications to join one of the tours of Great Britain and Ireland which are being organized for the week following the Congress must be received by February I5. All communications should be sent to the Secretary-General, 6th International Congress of Radiology, 45, Lincoln's Inn Fields, London, W.C.2. Additional copies of the Preliminary Programme can be obtained from the same address on request, stating the language in which they are desired.